Simplify each expression. Write answers using positive exponents.
a. (7x^2y^3)(-2xy)
b. (a^2b^3)^-1(a^2b^3)
c.(-4m^3)^2
I will be happy to check your work.
c. -16m^6
a. -14x^3y^4 ??
a. correct
c. oops: (-4)^2 = +16
To simplify each expression and write the answers using positive exponents, we can follow a few general rules of exponent arithmetic:
1. When multiplying two terms with the same base, add the exponents.
2. When dividing two terms with the same base, subtract the exponents.
3. When raising a power to another power, multiply the exponents.
Let's apply these rules to simplify each expression:
a. (7x^2y^3)(-2xy)
To simplify this expression, we can multiply the coefficients and add the exponents of the variables:
7 * -2 = -14
x^2 * x^1 = x^(2+1) = x^3
y^3 * y^1 = y^(3+1) = y^4
Therefore, the simplified expression is -14x^3y^4.
b. (a^2b^3)^-1(a^2b^3)
To simplify this expression, we can apply the rule for raising a power to another power:
(a^2b^3)^-1 * (a^2b^3)^1
Since the bases are the same, we can multiply the exponents within each set of parentheses:
a^(2 * -1) = a^(-2)
b^(3 * -1) = b^(-3)
Therefore, the simplified expression is a^(-2)b^(-3).
c. (-4m^3)^2
To simplify this expression, we can apply the rule for raising a power to another power:
(-4m^3)^2
Since the exponent is outside the parentheses, we need to multiply it by each exponent inside the parentheses:
(-4)^2 * (m^3)^2
Simplifying further:
(-4)^2 = 16
(m^3)^2 = m^(3 * 2) = m^6
Therefore, the simplified expression is 16m^6.